Thermal Hall conductance. The electronic Hall conductance, originating from the Kubo formula, is the integral of Berry curvature with an appropriate weight, which relates the anomalous velocity of the magnons, multiplied by the Fermi distribution function over all energies [1]}, [2]}. With this description, the topological phase is still included within the framework of Bloch's wave function and band theory, that is, topological band theory. Similarly, the thermal Hall conductance can be expressed as a weighted summation of the Berry curvature, according to linear response theory as [3]}, [4]}
\(\kappa _{xy}=-\frac{k_B^2 T}{\hbar a}\frac{1}{N}\sum _{\lambda \mathbf {k}} c_2(n_B(\varepsilon _{\lambda \mathbf {k}})) \Omega _{\lambda \mathbf {k}},\) 
